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Annotation 1729429638412

#pyro
The basic unit of Pyro programs is the stochastic function.
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Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
In [1]: # import some dependencies import torch from torch.autograd import Variable import pyro import pyro.distributions as dist Models in Pyro: From Primitive Distributions to Stochastic Functions¶ <span>The basic unit of Pyro programs is the stochastic function. This is an arbitrary Python callable that combines two ingredients: deterministic Python code; and primitive stochastic functions Concretely, a stochastic function can be any Python



Annotation 1729431735564

#pyro
Expressing models as stochastic functions in Pyro means that models can be composed, reused, imported, and serialized just like regular Python callables.
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Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
Torch nn.Module . Throughout the tutorials and documentation, we will often call stochastic functions models, since stochastic functions can be used to represent simplified or abstract descriptions of a process by which data are generated. <span>Expressing models as stochastic functions in Pyro means that models can be composed, reused, imported, and serialized just like regular Python callables. Without further ado, let’s introduce one of our basic building blocks: primitive stochastic functions. Primitive Stochastic Functions¶ Primitive stochastic functions, or distrib



Annotation 1729433308428

#pyro
Primitive stochastic functions, or distributions, are an important class of stochastic functions for which we can explicitly compute the probability of the outputs given the inputs.
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Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
s that models can be composed, reused, imported, and serialized just like regular Python callables. Without further ado, let’s introduce one of our basic building blocks: primitive stochastic functions. Primitive Stochastic Functions¶ <span>Primitive stochastic functions, or distributions, are an important class of stochastic functions for which we can explicitly compute the probability of the outputs given the inputs. Pyro includes a standalone library, pyro.distributions , of GPU-accelerated multivariate probability distributions built on PyTorch. This comes with various familiar distributions like



Annotation 1729434881292

#pyro
users can implement custom distributions by subclassing pyro.distributions.Distribution .
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Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
the inputs. Pyro includes a standalone library, pyro.distributions , of GPU-accelerated multivariate probability distributions built on PyTorch. This comes with various familiar distributions like the bernoulli and uniform distributions, but <span>users can implement custom distributions by subclassing pyro.distributions.Distribution . Using primitive stochastic functions is easy. For example, to draw a sample x from the unit normal distribution (0,1)N(0,1) we do the following: In [2]: mu = Variable(torc



Flashcard 1729441959180

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#pyro
Question
users can implement custom distributions by [...] pyro.distributions.Distribution .
Answer
subclassing

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users can implement custom distributions by subclassing pyro.distributions.Distribution .

Original toplevel document

Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
the inputs. Pyro includes a standalone library, pyro.distributions , of GPU-accelerated multivariate probability distributions built on PyTorch. This comes with various familiar distributions like the bernoulli and uniform distributions, but <span>users can implement custom distributions by subclassing pyro.distributions.Distribution . Using primitive stochastic functions is easy. For example, to draw a sample x from the unit normal distribution (0,1)N(0,1) we do the following: In [2]: mu = Variable(torc






Flashcard 1729454279948

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#pyro
Question
Expressing models as [...] in Pyro means that models can be composed, reused, imported, and serialized just like regular Python callables.
Answer
stochastic functions

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Expressing models as stochastic functions in Pyro means that models can be composed, reused, imported, and serialized just like regular Python callables.

Original toplevel document

Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
Torch nn.Module . Throughout the tutorials and documentation, we will often call stochastic functions models, since stochastic functions can be used to represent simplified or abstract descriptions of a process by which data are generated. <span>Expressing models as stochastic functions in Pyro means that models can be composed, reused, imported, and serialized just like regular Python callables. Without further ado, let’s introduce one of our basic building blocks: primitive stochastic functions. Primitive Stochastic Functions¶ Primitive stochastic functions, or distrib






Flashcard 1729455852812

Tags
#pyro
Question
[...] are an important class of stochastic functions for which we can explicitly compute the probability of the outputs given the inputs.
Answer
Primitive stochastic functions

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Primitive stochastic functions, or distributions, are an important class of stochastic functions for which we can explicitly compute the probability of the outputs given the inputs.

Original toplevel document

Models in Pyro: From Primitive Distributions to Stochastic Functions — Pyro Tutorials documentation
s that models can be composed, reused, imported, and serialized just like regular Python callables. Without further ado, let’s introduce one of our basic building blocks: primitive stochastic functions. Primitive Stochastic Functions¶ <span>Primitive stochastic functions, or distributions, are an important class of stochastic functions for which we can explicitly compute the probability of the outputs given the inputs. Pyro includes a standalone library, pyro.distributions , of GPU-accelerated multivariate probability distributions built on PyTorch. This comes with various familiar distributions like






Annotation 1731463089420

#english
Novelist Adam Langer skewers the publishing trade — and some of its recent trends — while digging toward something deeper.
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Book review: 'The Thieves of Manhattan' by Adam Langer - latimes
30+ years Terms of Service Privacy Policy YOU ARE HERE: LAT Home→Collections Book review: 'The Thieves of Manhattan' by Adam Langer <span>Novelist Adam Langer skewers the publishing trade — and some of its recent trends — while digging toward something deeper. July 18, 2010|By Ella Taylor, Special to the Los Angeles Times Email Share The Thieves of Manhattan A Novel Adam Langer Spiegel & Grau: 260 pp., $15 paper



Annotation 1731661532428

#dynamic-programming
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
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Memoization - Wikipedia
dia, the free encyclopedia Jump to: navigation, search Not to be confused with Memorization. "Tabling" redirects here. For the parliamentary procedure, see Table (parliamentary procedure). <span>In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing [1] . Although related to caching, memoi



Flashcard 1731663629580

Tags
#dynamic-programming
Question
[...] speeds up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
Answer
memoization

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In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur a

Original toplevel document

Memoization - Wikipedia
dia, the free encyclopedia Jump to: navigation, search Not to be confused with Memorization. "Tabling" redirects here. For the parliamentary procedure, see Table (parliamentary procedure). <span>In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing [1] . Although related to caching, memoi






Flashcard 1731665202444

Tags
#dynamic-programming
Question
memoization saves [...] by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
Answer
computational time

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In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.

Original toplevel document

Memoization - Wikipedia
dia, the free encyclopedia Jump to: navigation, search Not to be confused with Memorization. "Tabling" redirects here. For the parliamentary procedure, see Table (parliamentary procedure). <span>In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing [1] . Although related to caching, memoi






Flashcard 1731666775308

Tags
#dynamic-programming
Question
memoization speeds up computer programs by storing [...] and returning the cached result when the same inputs occur again.
Answer
results of expensive function calls

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In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.

Original toplevel document

Memoization - Wikipedia
dia, the free encyclopedia Jump to: navigation, search Not to be confused with Memorization. "Tabling" redirects here. For the parliamentary procedure, see Table (parliamentary procedure). <span>In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing [1] . Although related to caching, memoi






Flashcard 1731684601100

Tags
#dynamic-programming
Question
subproblem solutions are typically indexed by [...] to facilitate lookup.
Answer
input values

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tion, one simply looks up the previously computed solution, thereby saving computation time at the expense of a (hopefully) modest expenditure in storage space. (Each of the subproblem solutions is indexed in some way, typically based on <span>the values of its input parameters, so as to facilitate its lookup.) <span><body><html>

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Dynamic programming - Wikipedia
This article's factual accuracy is disputed. Relevant discussion may be found on the talk page. Please help to ensure that disputed statements are reliably sourced. (November 2015) (Learn how and when to remove this template message) <span>In computer science, mathematics, management science, economics and bioinformatics, dynamic programming (also known as dynamic optimization) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions. The next time the same subproblem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time at the expense of a (hopefully) modest expenditure in storage space. (Each of the subproblem solutions is indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup.) The technique of storing solutions to subproblems instead of recomputing them is called "memoization". Dynamic programming algorithms are often used for optimization. A dyna






Flashcard 1736002374924

Tags
#stochastics
Question
the index set and state space of Wiener process are [...] and [...], respectively
Answer
the non-negative numbers and real numbers

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Playing a central role in the theory of probability, the Wiener process is often considered the most important and studied stochastic process, with connections to other stochastic processes. [1] [2] [3] [78] [79] [80] [81] Its index set and state space are the non-negative numbers and real numbers, respectively, so it has both continuous index set and states space.

Original toplevel document

Stochastic process - Wikipedia
wnian motion due to its historical connection as a model for Brownian movement in liquids. [75] [76] [76] [77] [imagelink] Realizations of Wiener processes (or Brownian motion processes) with drift (blue) and without drift (red). <span>Playing a central role in the theory of probability, the Wiener process is often considered the most important and studied stochastic process, with connections to other stochastic processes. [1] [2] [3] [78] [79] [80] [81] Its index set and state space are the non-negative numbers and real numbers, respectively, so it has both continuous index set and states space. [82] But the process can be defined more generally so its state space can be n {\displaystyle n} -dimensional Euclidean space. [71] [79] [83]






Annotation 1758219603212

#calculus
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Taylor series - Wikipedia
l Line integral Surface integral Volume integral Jacobian Hessian matrix Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor seri



Flashcard 1758221700364

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#calculus
Question
Taylor series represent a function as an infinite sum of terms that are calculated from [...].
Answer
the values of the function's derivatives at a single point

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In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

Original toplevel document

Taylor series - Wikipedia
l Line integral Surface integral Volume integral Jacobian Hessian matrix Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor seri






Flashcard 1791855037708

Tags
#topology
Question
A set U is open if [...description...].
Answer
every point in U has a neighborhood contained in U

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U is open if every point in U has a neighborhood contained in U.

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Open set - Wikipedia
ntained in U. Metric spaces[edit] A subset U of a metric space (M, d) is called open if, given any point x in U, there exists a real number ε > 0 such that, given any point y in M with d(x, y) < ε, y also belongs to U. Equivalently, <span>U is open if every point in U has a neighborhood contained in U. This generalizes the Euclidean space example, since Euclidean space with the Euclidean distance is a metric space. Topological spaces[edit] In general topological spaces, the open






Annotation 1799060065548

#jaynes #plausible-reasoning
if A then B expresses B only as a logical consequence of A; not necessarily a causal physical consequence
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Flashcard 1799066619148

Tags
#has-images #jaynes #plausible-reasoning
Question
Given
A ≡ it will start to rain by 10 am at the latest;
B ≡ the sky will become cloudy before 10 am.

The strong syllogism takes the form [...]
[unknown IMAGE 1799062162700]

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Flashcard 1799068978444

Tags
#has-images #jaynes #plausible-reasoning
Question
Given
A ≡ it will start to rain by 10 am at the latest;
B ≡ the sky will become cloudy before 10 am.

The inverse of the strong syllogism takes the form [...]
[unknown IMAGE 1799063735564]

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Flashcard 1799070813452

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#has-images #jaynes #plausible-reasoning
Question
Given
A ≡ it will start to rain by 10 am at the latest;
B ≡ the sky will become cloudy before 10 am.

The weaker syllogism (B is true) takes the form [...]
[unknown IMAGE 1799065308428]

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Flashcard 1799073434892

Tags
#jaynes #plausible-reasoning
Question
if A then B expresses B only as a [...] of A; not necessarily a causal physical consequence
Answer
logical consequence

Think of A as rain and B as cloudy sky, B preceeds A

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if A then B expresses B only as a logical consequence of A; not necessarily a causal physical consequence

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Flashcard 1799075007756

Tags
#jaynes #plausible-reasoning
Question
if A then B expresses B only as a logical consequence of A; not necessarily a [...]
Answer
causal physical consequence

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if A then B expresses B only as a logical consequence of A; not necessarily a causal physical consequence

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